Is there an option to hide to all but admins and moderators when an admin or moderator unhides a topic which has been auto-hidden by the forum bot? The bot made a mistake and now my moderator action to unhide the topic is public.
You can delete the small action notifications. Then only mods/admins will have the ability to see the deleted small actions, no one else will see them
So there is no option to disable public moderator action “posts” to a topic?
Correct, the small posts will appear, there is no way to disable them. However, as @cpradio suggested you can immediately delete them if you wish.